"Hybrid queens have a chance to produce hybrid offspring, which have a chance to mutate into an entirely new species."
Cross-breeding is one of the main mechanics of the game, and allows the player to discover new species by cross-breeding different bees together.
Based on different critera, there's a chance for the cross-bred offspring to mutate into a new species.
When two different species are bred together they form a "Hybrid" Queen. When the Queen comes to the end of her Lifespan she'll produce offspring, which will also have a chance to be hybrids thanks to the ol' Punnett Square!
You can use a Predictor on a Queen to see the breakdown of offspring that she can produce, along with the chances for each offspring. The offspring of a hybrid queen will always have a 50% chance to be a hybrid (hybrid != mutation)
Depending on the two species of the hybrid and environmental factors, the hybrid offspring can mutate into a completely new species.
For example, to get a Verdant Bee, you need to have a Forest-Common offspring produced during the day.
To get some species of bee, the offspring need certain environmental factors like the time of day, or the weather - others need special conditions, like certain traits or nearby objects. The Apiarist's Almanac gives a hint for each undiscovered species on what these conditions are, as well as the two species that need to be cross-bred together.
Dr Beenjamin BhD will also give you a hints for any undiscovered bees in your book if you ask him for one!
Each species also has a per-species mutation "chance" that is rolled along with the special conditions, on top of the 50% hybrid chance. This per-species mutation chance can be turned off in the Accessibility options, which means Stability is no longer used. Turning this off doesn't affect progress or Achievements, it just simply removes the stability mechanic and the "grind" of mutations - however you will still need to roll the 50% hybrid offspring chance.